107 research outputs found
Tardos fingerprinting is better than we thought
We review the fingerprinting scheme by Tardos and show that it has a much
better performance than suggested by the proofs in Tardos' original paper. In
particular, the length of the codewords can be significantly reduced.
First we generalize the proofs of the false positive and false negative error
probabilities with the following modifications: (1) we replace Tardos'
hard-coded numbers by variables and (2) we allow for independently chosen false
positive and false negative error rates. It turns out that all the
collusion-resistance properties can still be proven when the code length is
reduced by a factor of more than 2.
Second, we study the statistical properties of the fingerprinting scheme, in
particular the average and variance of the accusations. We identify which
colluder strategy forces the content owner to employ the longest code. Using a
gaussian approximation for the probability density functions of the
accusations, we show that the required false negative and false positive error
rate can be achieved with codes that are a factor 2 shorter than required for
rigid proofs.
Combining the results of these two approaches, we show that the Tardos scheme
can be used with a code length approximately 5 times shorter than in the
original construction.Comment: Modified presentation of result
Optimal sequential fingerprinting: Wald vs. Tardos
We study sequential collusion-resistant fingerprinting, where the
fingerprinting code is generated in advance but accusations may be made between
rounds, and show that in this setting both the dynamic Tardos scheme and
schemes building upon Wald's sequential probability ratio test (SPRT) are
asymptotically optimal. We further compare these two approaches to sequential
fingerprinting, highlighting differences between the two schemes. Based on
these differences, we argue that Wald's scheme should in general be preferred
over the dynamic Tardos scheme, even though both schemes have their merits. As
a side result, we derive an optimal sequential group testing method for the
classical model, which can easily be generalized to different group testing
models.Comment: 12 pages, 10 figure
Enhanced blind decoding of Tardos codes with new map-based functions
This paper presents a new decoder for probabilistic binary traitor tracing
codes under the marking assumption. It is based on a binary hypothesis testing
rule which integrates a collusion channel relaxation so as to obtain numerical
and simple accusation functions. This decoder is blind as no estimation of the
collusion channel prior to the accusation is required. Experimentations show
that using the proposed decoder gives better performance than the well-known
symmetric version of the Tardos decoder for common attack channels
Dynamic Traitor Tracing for Arbitrary Alphabets: Divide and Conquer
We give a generic divide-and-conquer approach for constructing
collusion-resistant probabilistic dynamic traitor tracing schemes with larger
alphabets from schemes with smaller alphabets. This construction offers a
linear tradeoff between the alphabet size and the codelength. In particular, we
show that applying our results to the binary dynamic Tardos scheme of Laarhoven
et al. leads to schemes that are shorter by a factor equal to half the alphabet
size. Asymptotically, these codelengths correspond, up to a constant factor, to
the fingerprinting capacity for static probabilistic schemes. This gives a
hierarchy of probabilistic dynamic traitor tracing schemes, and bridges the gap
between the low bandwidth, high codelength scheme of Laarhoven et al. and the
high bandwidth, low codelength scheme of Fiat and Tassa.Comment: 6 pages, 1 figur
Asymptotically false-positive-maximizing attack on non-binary Tardos codes
We use a method recently introduced by Simone and Skoric to study accusation
probabilities for non-binary Tardos fingerprinting codes. We generalize the
pre-computation steps in this approach to include a broad class of collusion
attack strategies. We analytically derive properties of a special attack that
asymptotically maximizes false accusation probabilities. We present numerical
results on sufficient code lengths for this attack, and explain the abrupt
transitions that occur in these results
Optimal symmetric Tardos traitor tracing schemes
For the Tardos traitor tracing scheme, we show that by combining the
symbol-symmetric accusation function of Skoric et al. with the improved
analysis of Blayer and Tassa we get further improvements. Our construction
gives codes that are up to 4 times shorter than Blayer and Tassa's, and up to 2
times shorter than the codes from Skoric et al. Asymptotically, we achieve the
theoretical optimal codelength for Tardos' distribution function and the
symmetric score function. For large coalitions, our codelengths are
asymptotically about 4.93% of Tardos' original codelengths, which also improves
upon results from Nuida et al.Comment: 16 pages, 1 figur
Worst case attacks against binary probabilistic traitor tracing codes
An insightful view into the design of traitor tracing codes should
necessarily consider the worst case attacks that the colluders can lead. This
paper takes an information-theoretic point of view where the worst case attack
is defined as the collusion strategy minimizing the achievable rate of the
traitor tracing code. Two different decoders are envisaged, the joint decoder
and the simple decoder, as recently defined by P. Moulin
\cite{Moulin08universal}. Several classes of colluders are defined with
increasing power. The worst case attack is derived for each class and each
decoder when applied to Tardos' codes and a probabilistic version of the
Boneh-Shaw construction. This contextual study gives the real rates achievable
by the binary probabilistic traitor tracing codes. Attacks usually considered
in literature, such as majority or minority votes, are indeed largely
suboptimal. This article also shows the utmost importance of the time-sharing
concept in a probabilistic codes.Comment: submitted to IEEE Trans. on Information Forensics and Securit
Capacities and Capacity-Achieving Decoders for Various Fingerprinting Games
Combining an information-theoretic approach to fingerprinting with a more
constructive, statistical approach, we derive new results on the fingerprinting
capacities for various informed settings, as well as new log-likelihood
decoders with provable code lengths that asymptotically match these capacities.
The simple decoder built against the interleaving attack is further shown to
achieve the simple capacity for unknown attacks, and is argued to be an
improved version of the recently proposed decoder of Oosterwijk et al. With
this new universal decoder, cut-offs on the bias distribution function can
finally be dismissed.
Besides the application of these results to fingerprinting, a direct
consequence of our results to group testing is that (i) a simple decoder
asymptotically requires a factor 1.44 more tests to find defectives than a
joint decoder, and (ii) the simple decoder presented in this paper provably
achieves this bound.Comment: 13 pages, 2 figure
On the Saddle-point Solution and the Large-Coalition Asymptotics of Fingerprinting Games
We study a fingerprinting game in which the number of colluders and the
collusion channel are unknown. The encoder embeds fingerprints into a host
sequence and provides the decoder with the capability to trace back pirated
copies to the colluders.
Fingerprinting capacity has recently been derived as the limit value of a
sequence of maximin games with mutual information as their payoff functions.
However, these games generally do not admit saddle-point solutions and are very
hard to solve numerically. Here under the so-called Boneh-Shaw marking
assumption, we reformulate the capacity as the value of a single two-person
zero-sum game, and show that it is achieved by a saddle-point solution.
If the maximal coalition size is k and the fingerprinting alphabet is binary,
we show that capacity decays quadratically with k. Furthermore, we prove
rigorously that the asymptotic capacity is 1/(k^2 2ln2) and we confirm our
earlier conjecture that Tardos' choice of the arcsine distribution
asymptotically maximizes the mutual information payoff function while the
interleaving attack minimizes it. Along with the asymptotic behavior, numerical
solutions to the game for small k are also presented.Comment: submitted to IEEE Trans. on Information Forensics and Securit
- …